## I329 - Algebras, Coalgebras and Processes

#### Course information

Instructor: Assoc.Prof. Uwe Wolter Uwe.Wolter@ii.uib.no Room 4102 Tel. 555 84 196
Lectures: Monday 12.15 - 14.00 (Grupperom 2103, HiB)
Thursday 10.15 - 12.00 (Grupperom 2103, HiB)
Forelesningene vil bli holdt på engelsk/The lectures will be given in English.
Start: 25. August, Monday 12.15 - 14.00 (Grupperom 2103, HiB)
Exam: The exam will be oral.

#### Course description

Content: Universal Algebra is one of the fundaments of Computer Science. Especially, it is used to describe in an abstract way data types and static aspects of programs and systems.
In the seminar I will discuss basic concepts of Universal Algebra as signatures, algebras, homomorphisms, terms, term algebrsas, induction.
Besides the static aspects we also have to describe the dynamic aspects, i.e., the behaviour, of programs and systems. Different concepts of processes have been developed the last 40 years to reason about the behaviour of systems.
Surprisingly, it turned out the last few years that processes are strongly related to coalgebras, the dual of algebras.
In the seminar I will present this duality based on a categorical reformulation of the basic concepts of Universal Algebra. Moreover I will give a coalgebraic analysis of the deterministic processes of CSP (Communicating Sequential Processes).
Prerequisites: Since the duality of algebras and coalgebras will be described on a categorical level some basic knowledge in Category Theory is recommended. Especially, I will use the following concepts: Category, functor, natural transformation, initial and terminal object, product, coproduct, limit, colimit.
Here you can find something about these concepts Elements of Basic Category Theory.

#### Course material

The main source for the exam will be your lecture notes. But, during the seminar I will provide you with some articles that may be helpful for understanding and for private studies.
Here you can have a look at a Tutorial on (Co)Algebras and (Co)Induction to get an impression what the seminar will be about.